In game theory, the stag hunt is a game which describes a conflict between safety and social cooperation. Other names for it or its variants include "assurance game", "coordination game", and "trust dilemma". Jean-Jacques Rousseau described a situation in which two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each player must choose an action without knowing the choice of the other. If an individual hunts a stag, he must have the cooperation of his partner in order to succeed. An individual can get a hare by himself, but a hare is worth less than a stag. This is taken to be an important analogy for social cooperation.
The stag hunt differs from the Prisoner's Dilemma in that the greatest potential payoff is both players cooperating, whereas in the prisoners Dilemma, the greatest payoff is in one player cooperating, and the other defecting.
An example of the payoff matrix for the stag hunt is pictured in Figure 2.

The stag hunt and social cooperation
In addition to the example suggested by Rousseau, David Hume provides a series of examples that are stag hunts. One example addresses two individuals who must row a boat. If both choose to row they can successfully move the boat. However if one doesn't, the other wastes his effort. Hume's second example involves two neighbors wishing to drain a meadow. If they both work to drain it they will be successful, but if either fails to do his part the meadow will not be drained.
There are several animal behaviors that have been described as stag hunts. For example, the coordination of slime molds. In times of stress, individual unicellular protists will aggregate to form one large body. Here if they all act together they can successfully reproduce, however the success depends on the cooperation of many bacteria. Also, the hunting practices of orca (known as carousel feeding) are an example of a stag hunt. Here orcas cooperatively corral large schools of fish to the surface and stun them by hitting them with their tails. Since this requires that fish not have any mechanism for escape, it requires the cooperation of many orcas.